Constant Modulus Algorithm Based on Different Error Functions Weighted by Variable Coefficient

2011 ◽  
Vol 66-68 ◽  
pp. 1579-1585
Author(s):  
Qiao Xi Zhou ◽  
Ye Cai Guo
Keyword(s):  
Theoretical Analysis ◽  
Convergence Rate ◽  
Variable Coefficient ◽  
Gradient Descent ◽  
Error Function ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Error Functions

To improve equalization performance of the constant modulus algorithm (CMA), we study that error functions have an influence on the performance of the algorithm in this paper. Aiming at the character of different error functions, a new style of error function weighted by a variable coefficient is proposed. And a new CMA based on the new error function (VCMA) is proposed too. Because of variable-coefficient adjustability, the value of this new error function can become larger at the beginning of iteration and smaller at the end of iteration in the new algorithm. From gradient descent method, VCMA can have faster convergence rate and lower residual error than the CMA. Both theoretical analysis and experimental results have shown the effectiveness of the proposed algorithm.

scholarly journals ANN based method for improving gold price forecasting accuracy through modified gradient descent methods

2020 ◽  
Vol 9 (1) ◽  
pp. 46
Author(s):  
Shilpa Verma ◽  
G. T. Thampi ◽  
Madhuri Rao
Keyword(s):  
Gradient Descent ◽  
Likelihood Function ◽  
Error Function ◽  
Complex Problem ◽  
Descent Method ◽  
Gold Price ◽  
Price Forecasting ◽  
Gradient Descent Method ◽  
Forecasting Accuracy ◽  
Median Error

Forecast of prices of financial assets including gold is of considerable importance for planning the economy. For centuries, people have been holding gold for many important reasons such as smoothening inflation fluctuations, protection from an economic crisis, sound investment etc.. Forecasting of gold prices is therefore an ever important exercise undertaken both by individuals and groups. Various local, global, political, psychological and economic factors make such a forecast a complex problem. Data analysts have been increasingly applying Artificial Intelligence (AI) techniques to make such forecasts. In the present work an inter comparison of gold price forecasting in Indian market is first done by employing a few classical Artificial Neural Network (ANN) techniques, namely Gradient Descent Method (GDM), Resilient Backpropagation method (RP), Scaled Conjugate Gradient method (SCG), Levenberg-Marquardt method (LM), Bayesian Regularization method (BR), One Step Secant method (OSS) and BFGS Quasi Newton method (BFG). Improvement in forecasting accuracy is achieved by proposing and developing a few modified GDM algorithms that incorporate different optimization functions by replacing the standard quadratic error function of classical GDM. Various optimization functions investigated in the present work are Mean median error function (MMD), Cauchy error function (CCY), Minkowski error function (MKW), Log cosh error function (LCH) and Negative logarithmic likelihood function (NLG). Modified algorithms incorporating these optimization functions are referred to here by GDM_MMD, GDM_CCY, GDM_KWK, GDM_LCH and GDM_NLG respectively. Gold price forecasting is then done by employing these algorithms and the results are analysed. The results of our study suggest that  the forecasting efficiency improves considerably on applying the modified methods proposed by us.

scholarly journals Predicting the Number of COVID-19 Sufferers in Malang City Using the Backpropagation Neural Network with the Fletcher–Reeves Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Syaiful Anam ◽  
Mochamad Hakim Akbar Assidiq Maulana ◽  
Noor Hidayat ◽  
Indah Yanti ◽  
Zuraidah Fitriah ◽  
...  
Keyword(s):  
Neural Network ◽  
Convergence Rate ◽  
Gradient Descent ◽  
Infected Individual ◽  
Prediction Method ◽  
Optimization Method ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Backpropagation Neural Network ◽  
Congenital Diseases

COVID-19 is a type of an infectious disease that is caused by the new coronavirus. The spread of COVID-19 needs to be suppressed because COVID-19 can cause death, especially for sufferers with congenital diseases and a weak immune system. COVID-19 spreads through direct contact, wherein the infected individual spreads the COVID-19 virus through cough, sneeze, or close contacts. Predicting the number of COVID-19 sufferers becomes an important task in the effort to curb the spread of COVID-19. Artificial neural network (ANN) is the prediction method that delivers effective results in doing this job. Backpropagation, a type of ANN algorithm, offers predictive problem solving with good performance. However, its performance depends on the optimization method applied during the training process. In general, the optimization method in ANN is the gradient descent method, which is known to have a slow convergence rate. Meanwhile, the Fletcher–Reeves method has a faster convergence rate than the gradient descent method. Based on this hypothesis, this paper proposes a prediction model for the number of COVID-19 sufferers in Malang using the Backpropagation neural network with the Fletcher–Reeves method. The experimental results show that the Backpropagation neural network with the Fletcher–Reeves method has a better performance than the Backpropagation neural network with the gradient descent method. This is shown by the Means Square Error (MSE) resulting from the proposed method which is smaller than the MSE resulting from the Backpropagation neural network with the gradient descent method.

scholarly journals Estimation of Navigation Mark Floating Based on Fractional-Order Gradient Descent with Momentum for RBF Neural Network

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qionglin Fang
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Gradient Descent ◽  
Rbf Neural Network ◽  
Error Function ◽  
Initial Position ◽  
Descent Method ◽  
Local Optimum ◽  
Gradient Descent Method ◽  
The Neural Network

To address the difficulty of estimating the drift of the navigation marks, a fractional-order gradient with the momentum RBF neural network (FOGDM-RBF) is designed. The convergence is proved, and it is used to estimate the drifting trajectory of the navigation marks with different geographical locations. First, the weight of the neural network is set. The navigation mark’s meteorological, hydrological, and initial position data are taken as the input of the neural network. The neural network is trained and used to estimate the mark’s position. The navigation mark’s position is taken at a later time as the output of the neural network. The difference between the later position and the estimated position obtained from the neural network is the error function of the neural network. The influence of sea conditions and months are analyzed. The experimental results and error analysis show that FOGDM-RBF is better than other algorithms at trajectory estimation and interpolation, has better accuracy and generalization, and does not easily fall into the local optimum. It is effective at accelerating convergence speed and improving the performance of a gradient descent method.

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